650 PHILOSOPHICAL TRANSACTIONS. [aNNO 1775. 



6. If pqn be a quadrant; that is, \{dhe=:r, the whole time of descent from 

 p to n will be = — t: X (e — f), by the above theorem. Which time, by what 



I have shown in the Philos. Trans, for 177 Ij '® = "77 ^ ("s-e + -s- ^^^ — 2c), 

 c being -^ of the periphery of the circle whose radius is r. Consequently, 

 -^T X (e — f) being found = — x (iE + -i.v' e^ — 2c), we find from that equa- 

 tion F = -I^E — 4-'^E^ — 2c, where e is the quadrantal arc of the ellipsis, whose 

 semi-transverse and semi-conjugate axes are ^2r and -/r; and p the quadrantal 

 arc of another ellipsis, whose semi-transverse and semi-conjugate axes are 

 \/ J + 4^/r and a/^— Wr. 



Before Mr. Maclaurin published his Treatise of Fluxions, some eminent ma- 

 thematicians imagined that the elastic curve could not be constructed by the qua- 

 drature or rectification of the conic sections. But that gentleman has showed in 

 that treatise, that the said curve may in every case be constructed by the rectifi- 

 cation of the hyperbola and ellipsis; and he has observed that, by the same 

 means, we may construct the curve along which, if a heavy body moved, it 

 would recede equally in equal times from a given point. Which last mentioned 

 curve Mr. James Bernoulli constructed by the rectification of the elastic curve, 

 and Mr. Leibnitz and Mr. John Bernoulli by the rectification of a geometrical 

 curve of a higher kind than the conic sections. It is observable, that Mr. 

 Maclaurin's method of construction just now adverted to, though very elegant, 

 is not without a defect. The difference between the hyperbolic arc and its tan- 

 gent being necessary to be taken, the method always fails when some principal 

 point in the figure is to be determined ; the said arc and its tangent then both 

 becoming infinite, though their difference be at the same time finite. The con 

 tents of this paper properly applied, will evince that both the elastic curve, and 

 the curve of equable recess from a given point, with many others, may be con- 

 structed by the rectification of the ellipsis only, without failure in any point. 



XXVII. Astronomical Observations made at Chislehurst, in Kent, in the Year 

 1774. By the Rev. Francis Wollaslon, LL.B., F. R. S. p. 290. 

 Mr. W. having now completed his original design, and kept his clock going 

 for a 3d year, without the least touch of the oil, or any alteration whatever, he 

 presumes the result of his observations to ascertain the rate of its going, may 

 not be an unacceptable addition to the former papers on that subject, delivered 

 to the Society. The regular difference between the summer and winter months, 

 and some degree of similarity between those differences, seems to show a regu- 

 larity in the cause. What that may be, is not fully to be ascertained by these 

 observations; though it seems to have been difference of moisture, rather than 



